Sunday, July 29, 2012

Newman: What Russell’s Structural Argument Needs

[UPDATE: 15 May 2013; edited for clarity]
As mentioned earlier here, Bertrand Russell’s work in his book The Analysis of Matter was dealt a blow by mathematician M.H.A."Max"Newman. Russell had built an argument supporting partial realism about the physical world. He said that while we are only acquainted with our percepts, there are causal connections between these and unperceived events external to the perceiver. He gave reasons to think that as a result, a system of relations among percepts can share the same structure as that of causally connected but unperceived events. We can therefore infer a great deal about the structure of the physical world. Newman pointed out that using conventional set-theoretic definitions of these terms, a shared structure in fact would not offer much information at all about the external world; formally any collection of things (of a sufficient cardinality) can be organized in relations so as to have a given structure.

Newman’s clearly argued and thoughtful paper, “Mr. Russell’s Causal Theory of Perception,” (also posted here) while delivering a negative result on this crucial point, was nonetheless sympathetic toward Russell’s project. Newman offered a suggestion as to what would be required in order to have a more meaningful result. He said we need to have, in addition to our individual percepts and the notion of a shared structure, some direct acquaintance with relations (and he points out that in some passages this sort of “modified theory” is what Russell seems to have in mind):

The conclusion that has been reached is that to maintain the view that something besides their existence can be known about the unperceived parts of the world it is necessary to admit direct apprehension of what is meant by the statement that two unperceived events are causally adjoined, i.e., happen near each other, temporally and spatially, or overlap, or do something of the sort. The central doctrine is then that while of percepts we have a qualitative knowledge, of other events all that can legitimately be inferred is their structure with regard to a certain directly known relation which may be called “causal proximity”(p.148 emphasis original)

In addition to the abstract structure, knowledge of the relation of causal proximity would give us leverage to extend our knowledge to the specific system of causal relations among the unperceived events (though still not their intrinsic qualities, in line with the “clear-cut” unmodified theory).
Newman also points out potential disadvantages of introducing this modification: it adds an additional primitive notion of acquaintance or “direct apprehension” which needs to be better defined; it also might open the door to questioning why we can’t invoke even more sorts of direct knowledge of non-structural aspects of the world.
He concluded the paper in this way:

It appears, then, that although a modified form of Mr. Russell’s theory makes an important assertion about our knowledge of the external world, a good deal of further argument will be necessary to show that this assertion is true. (p.148)

Russell wrote a letter to Newman following the publication of this paper (it is included in the second volume of Russell’s autobiography). In the letter, Russell conceded the argument and went on to say:

It was quite clear to me, as I read your article, that I had not really intended to say what in fact I did say, that nothing is known about the physical world except its structure. I had always assumed spacio-temporal continuity with the world of percepts, that is to say, I had assumed that there might be co-punctuality between percepts and non-percepts, and even that one could pass by a finite number of steps from one event to another compresent with it, from one end of the universe to another. And co-punctuality I regarded as a relation which might exist among percepts and is itself perceptible. (p. 259, emphasis original).

Newman’s commentary above sketches a notion of perceiving “causal proximity” or the idea of events being spatio-temporally near each other or perhaps overlapping. Russell singles out the notion of perceiving co-punctuality. If events overlap or are simultaneous, perhaps the notion of directly perceiving a relation between them is explicable.

As I discussed before, Russell’s later book, Human Knowledge, did conclude that we must have some primitive (“animal” or “biological”) grasp of causation in order to have scientific knowledge. He also reiterated key themes from The Analysis of Matter (including, for example, the role of simultaneity in his theory of compresence). I didn’t see in my reading, though, that he specifically built on the notion of perceiving causal relations via co-punctuality as discussed in his letter to Newman.